Theorem orim2d 789

Description: Disjoin antecedents and consequents in a deduction. (Contributed by NM, 23-Apr-1995.)

Hypothesis

Ref	Expression
orim1d.1	|- ( ph -> ( ps -> ch ) )

Assertion

Ref	Expression
orim2d	|- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Proof of Theorem orim2d

Step	Hyp	Ref	Expression
1		idd 21	. 2 |- ( ph -> ( th -> th ) )
2		orim1d.1	. 2 |- ( ph -> ( ps -> ch ) )
3	1, 2	orim12d 787	1 |- ( ph -> ( ( th \/ ps ) -> ( th \/ ch ) ) )

Syntax hints:   -> wi 4   \/ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  orim2  790  orbi2d  791  pm2.82  813  stdcndcOLD  847  pm2.13dc  886  exmid1dc  4212  acexmidlemcase  5883  poxp  6247  fodjuomnilemdc  7156  omniwomnimkv  7179  exmidontriimlem1  7234  indpi  7355  suplocexprlemloc  7734  nneoor  9369  uzp1  9575  maxabslemlub  11230  xrmaxiflemlub  11270  exmidunben  12441  bj-nn0suc  15069  sbthomlem  15127